Related papers: Fully self-consistent optimized effective potentia…
We study the question of existence and uniqueness for the finite temperature Kohn-Sham equations. For finite volumes, a unique soluion is shown to exists if the effective potential satisfies a set of general conditions and the coupling…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
This is a brief description of how to derive the local ``atomic'' potentials from the Self-Consistent Atomic Deformation (SCAD) model density function. Particular attention is paid to the spherically averaged case.
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the…
The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is…
A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. {\bf 136}, 224109 (2012)]. As illustrated, a convenient…
One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the…
It is shown here that Kohn-Sham equations cannot be derived from Hohenberg-Kohn theory without an additional postulate. Assuming that a functional derivative with respect to total electron density exists leads in general to a theory…
In a recent Letter, Baer et al. present a stochastic method for Kohn-Sham density functional theory calculations. Their convergence criterion is the self-averaging total energy per electron, which requires a number of statistical samples…
For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential $V_{\mathrm{xc}\sigma}(\re)$ must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very…